Question: Solve for $x$ : $6x^2 - 6x - 12 = 0$
Explanation: Dividing both sides by $6$ gives: $ x^2 {-1}x {-2} = 0 $ The coefficient on the $x$ term is $-1$ and the constant term is $-2$ , so we need to find two numbers that add up to $-1$ and multiply to $-2$ The two numbers $1$ and $-2$ satisfy both conditions: $ {1} + {-2} = {-1} $ $ {1} \times {-2} = {-2} $ $(x + {1}) (x {-2}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 1) (x -2) = 0$ $x + 1 = 0$ or $x - 2 = 0$ Thus, $x = -1$ and $x = 2$ are the solutions.